Generalized Complex Submanifolds

Details Generalized Complex Submanifolds Generalized Complex Submanifolds

2006-03-20

arxiv.org/abs/math/0603480v3

Pacific J. Math. 236 (2008), no. 1, 23--44

Mathematics

Differential Geometry

section 3 expanded, three sections added, 19 pages

Scientific paper

10.2140/pjm.2008.236-1

We introduce the notion of twisted generalized complex submanifolds and describe an equivalent characterization in terms of Poisson-Dirac submanifolds. Our characterization recovers a result of Vaisman. An equivalent characterization is also given in terms of spinors. As a consequence, we show that the fixed locus of an involution preserving a twisted generalized complex structure is a twisted generalized complex submanifold. We also prove that a twisted generalized complex manifold has a natural Poisson structure. We also discuss generalized Kaehler submanifolds.

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